WCI’s analysis is based on Roth vs. Taxable.
For many investors Roth acconts are a small subset of their tax advantaged accounts.

The same analysis based on 401k vs. Taxable would show that bonds belong to the 401k

Read his reply to comments made to that effect. I posted them above. The outcome is the same.

“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

Read his reply to comments made to that effect. I posted them above. The outcome is the same.

I read his replies. His analysis is baloney for many investors who don't think about things for themselves. For instance, one thing to think about is tax rates while contributing and tax rates while withdrawing. His analysis may be OK for highly paid physicians who will work until they die or have a high tax bracket in retirement. I don't fall into that category.

His follow-on article attenuated the title of the original article, too.

Of course, if folks don't invest tax-efficiently in taxable with their stock funds, then it is likely that stock funds may not be best in taxable for those folks. Because I haven't paid any significant taxes on my taxable account investments in more than 10 years, I consider my taxable account an extension of my Roth IRA.

Last edited by livesoft on Sat Dec 09, 2017 7:15 pm, edited 1 time in total.

People always debate this issue with a set of assumptions which then don't hold for others. The factors that should be considered are:

- Capital gains tax rates vs income tax rates (Traditional account withdrawls get taxed as income; capital gains is less)
- Personal tax rates now vs retirement. (This is called tax arbitrage)
- How much in muni bonds you are comfortable holding. (Some people don't mind holding 100% of bond AA in munis. I stay at 20-30%)
- The immediate tax cost of income now vs in the future.

You'll find that the "bonds in taxable" crowd assumes it's safe to hold 100% of bonds in munis. They then assume someone won't be able to benefit greatly from tax arbitrage.

For someone retiring early (like me) bonds go in tax advantaged. It's not even close.

One can make some simple assumptions; an idealized version of reality, so to speak.
All stocks dividends are qualified and stocks do not distribute cg.
All bonds dividends are taxed at marginal rate and all return is from dividends.
Yearly stock return is a few % higher than bonds on average.
Investor tax rate stays constant.

As such, it is immediate to see that for equal amounts invested in stocks and bonds

excellent post by livesoft above
Also, one has to look at tax equivalent yield of munis if one is in higher brackets
Also, one has to look at the relative tax efficiency of the dividend yield of stock funds vs tax equivalent muni yield if one is in higher brackets
basically, the wiki is flawed
also matters if you are looking at after tax asset allocation, and adjusting for it

[*]Given the above to points, isn't it reasonably straightforward to calculate which placement should yield the most after tax return?

In a sense, I believe this was done in a general manner back in early Boglehead times. It is likely discussed in the original book which I don't have any more. I was not there, but it was posted later that stocks should go into taxable (after everything else was filled up) for two reasons.

First, putting bonds in taxable meant either paying tax on dividends (tax drag) for lower income people or using tax-exempt bonds for higher income people. Over the long run, after tax yield was higher for taxable bonds in 401k/IRA than tax-exempt bonds in taxable.

There are times this is not true - tax exempt bonds pay a little better in some time periods. So if you want to flip flop as times change, go ahead. If you don't want to flip flop, just use taxable bonds and keep them in tax-advantaged accounts because that was a better choice more often than the reverse. It should be noted that the "bonds go in taxable" argument happened during a time when tax-exempt bonds did have an advantage.

The second reason for stocks to go in taxable is that gains from stocks get taxed as ordinary income in a 401k/IRA instead of at the lower capital gains rates. Why do that? Stocks should be in taxable for the lower tax rate.

Long story short, there was a reason to let stocks overflow into taxable instead of bonds and there was a reason to not let bonds overflow into taxable instead of stocks.

This is how I remember it being explained at the time that "bonds should go in taxable" discussion started.

Yet a fair comparison has to assume equal allocations (as in the case of Roth vs. Taxable)

So the two cases to compare should be

400 stocks + 100 bonds tax-deferred
300 bonds taxable

Vs.

400 bonds + 100 stocks tax deferred
300 stocks taxable

And here it is immediate to see that it is the second allocation which comes out a winner.

It's not so obvious to me. Assuming a fixed 40% tax rate now and in the future, you have 500 in tax deferred which will be taxed at 40% when you withdraw. The amounts in the taxable are after tax, so only the growth will be taxed at 40% going forward.

First off, 400 stock + 100 bonds tax-deferred after tax is 240 stock + 60 bonds, which means an AA of 40/60 after tax adjustment. The second is an allocation of 60/40, so if you mean having more equities is likely to give you better returns, it's not surprising.

IMO, equal allocations as you've set them up here do not represent the same after tax AA and are not a fair comparison.

1. Assume no tax-loss harvesting.
2. Let's do the analysis for Roth, so that point is a wash.
3. If roth, then this is also a wash.
4. Let's use QDI of 15%
5. 25%
6. Let's forget about this.
7. Assume 100% in Roth.
8. Assume 100% in Roth.
9. For the moment, let's look just at accumulation and try to answer which gives most income at retirement.

One can make some simple assumptions; an idealized version of reality, so to speak.
All stocks dividends are qualified and stocks do not distribute cg.
All bonds dividends are taxed at marginal rate and all return is from dividends.
Yearly stock return is a few % higher than bonds on average.
Investor tax rate stays constant.

As such, it is immediate to see that for equal amounts invested in stocks and bonds

The advice to put stocks, rather than bonds, into taxable accounts come straight from the Wiki.

If investors are trying to minimize their taxes, then this strategy is fine. But if their strategy is to maximize their after-tax wealth, it is probably sub-optimal.

The White Coat Investor has demonstrated how, when using some very simple and straightforward assumptions (e.g. stocks' will outperform bonds in terms of total return in the long-run), bonds should be placed in taxable accounts instead of stocks. There are obviously some factors that can complicate this issue, but it seems to me that the 'default' position should be that bonds go in taxable, especially in the current environment where bonds produce such little income.

I'm beginning to question the rule of thumb that stocks should always be in taxable account.

There is no such rule of thumb. I don't know where people are getting this idea...you are certainly not the first. If it is from our Wiki page, it needs to be edited.

The rule of thumb is more like... "Fill your tax-advantaged accounts like 401k, IRA, Roth IRA with stocks and bonds. When they get full and you have more to save, put stocks in taxable." There are some who put both stocks and bonds in taxable.

I think that I am questioning even your updated rule of thumb, at-least when the choice is between Roth 401(k) and Taxable.

Stocks are intrinsically more tax efficient than bonds, therefore it makes sense to generally place bonds in tax advantaged accounts, rather than stocks (assuming one cannot put both).

Stock gains come mostly in the form of capital gains that the long term investor can choose to keep unrealized and therefore not subject to taxation.
Furthermore, QDI and LTG have their own asvantageous federal tax rate, if they are in a taxable account. If one puts them in a 401k, they will be taxed as income, at the marginal rate.

That said, it is always proper to examine carefully each individual situation instead of blindly trusting “rules”.

Yes, but efficiency by tax rate is not necessarily the metric to use. I think what you care is minimizing the total amount of tax paid, which is rate*taxable income.

Just to make the point by analogy, imagine that you have two routes to drive home along, one along a highway where you get better mpg. It would be a mistake to immediately conclude that the highway is the preferable route because you gas consumption rate is lower their. If the highway is a longer route, it might mean that you consume more gallons getting home even though your mpg is better along that route.

The analogous bits are taxable rate --- mpg, and then taxable income --- miles driven.

I'm beginning to question the rule of thumb that stocks should always be in taxable account. I agree that it minimizes your tax rate (in percentage) but thats not what we actually care about, correct? Don't we care about minimizing the total principal we pay to the gov (i.e. tax rate * tax income)?

Lets say bonds yield 2% real, and my marginal rate is 25%. Holding $100 of bonds in taxable brokerage means that I have after one year 100+2*.75=101.5. So my after-tax real growth rate is 1.5% if I hold bonds in taxable.

Lets say that stocks yield 5% real, and my long-term cap gains rate is 15%. Holding $100 of stocks in taxable brokerage means that I have after one year 100+5*.85=104.25. So my after-tax real growth rate is 4.25% if I hold stocks in taxable (and sold them after one year to fund expenses).

If I held the bonds in roth, I recapture 0.5% of growth per year? If I hold stocks in roth, I recapture .75% of growth per year. Doesn't that mean that, when deciding wether or not it is better to hold stocks or bonds in taxable, I have to look at the difference between the long-term capital gains rate and my marginal rate, and then also look at the expected difference between bonds and stocks growth rate?

Let me know your thoughts,

-kehyler

Edit: Let's assume that I have already filled all my tax-advantaged accounts.

Isn’t that 0.5% bond savings compounding, while the LTCG stock savings is not?

I'm beginning to question the rule of thumb that stocks should always be in taxable account.

There is no such rule of thumb. I don't know where people are getting this idea...you are certainly not the first. If it is from our Wiki page, it needs to be edited.

The rule of thumb is more like... "Fill your tax-advantaged accounts like 401k, IRA, Roth IRA with stocks and bonds. When they get full and you have more to save, put stocks in taxable." There are some who put both stocks and bonds in taxable.

I think that I am questioning even your updated rule of thumb, at-least when the choice is between Roth 401(k) and Taxable.

My "updated" rule of them does not really include Roth 401k except for people in the very low tax brackets. Everybody else should probably be using traditional 401k.

But, even if it did, Roth 401k has a clear benefit over taxable unless the Roth 401k plan has very high costs. Costs being equal or even close to equal, Roth accounts give you more money than taxable accounts.

I think what you care is minimizing the total amount of tax paid, which is rate*taxable income.

It is not as simple as that. Tax paid is not the right metric either. Money you have in the end is the right metric. There are some very simple examples of paying more tax but ending up with more money in the end.

I think what you care is minimizing the total amount of tax paid, which is rate*taxable income.

It is not as simple as that. Tax paid is not the right metric either. Money you have in the end is the right metric. There are some very simple examples of paying more tax but ending up with more money in the end.

Interesting, if they are pertinent to the situation at hand, mind sharing one or two?

The most common example is comparing tax-deferred to Roth. Let's start with $1,000, the 25% tax bracket, and a growth rate of doubling.

Tax deferred: You invest your $1k, it doubles to $2k, and is taxed at 25% as you take it out of the tax-deferred account. You pay $500 in tax and end up with $1,500.

Roth: You pay $250 tax on the front end, invest the $750 which doubles to $1,500 which is what you end up with.

In this example, you pay different amounts of tax and end up with the same amount of money. Not exactly the example you asked for but a good example of "it's not how much tax you pay, but how much money you end up with" that should be your metric.

Example 2. You start with $1k, your tax rate while working is 25%, your money doubles and your tax rate is 15% in retirement.

If you put the money in a taxable account, you pay $250 in tax and invest the remaining $750 which doubles to $1,500.

If you put the money in a tax-deferred account, your $1,000 doubles to $2,000 which is then taxed at 15% as you take it out. You end up with $1,700 even though you paid $300 in taxes. This is an example of paying more in taxes but ending up with more money in the end.

My point is that it is not about how many dollars you pay in tax. It is about the money you end up with.

I think what you care is minimizing the total amount of tax paid, which is rate*taxable income.

It is not as simple as that. Tax paid is not the right metric either. Money you have in the end is the right metric. There are some very simple examples of paying more tax but ending up with more money in the end.

Interesting, if they are pertinent to the situation at hand, mind sharing one or two?

I begin with $10,000 of pre-tax money. Let's pretend my IRA marginal withdrawal rate will be 25%, the same as the contribution deduction rate. Assume 5% annual return and 0.25% tax drag in taxable account, with 15% LTCG rate. Funds are withdrawn after 30 years. This is all pretty reasonable. I can choose between putting my money in a deductible tIRA or in taxable.

Yes, but efficiency by tax rate is not necessarily the metric to use. I think what you care is minimizing the total amount of tax paid, which is rate*taxable income.

Just to make the point by analogy, imagine that you have two routes to drive home along, one along a highway where you get better mpg. It would be a mistake to immediately conclude that the highway is the preferable route because you gas consumption rate is lower their. If the highway is a longer route, it might mean that you consume more gallons getting home even though your mpg is better along that route.

The analogous bits are taxable rate --- mpg, and then taxable income --- miles driven.

But the pre-tax return of a given AA is fixed. Therefore if I pay less taxes I end up with more money.

Yes, but efficiency by tax rate is not necessarily the metric to use. I think what you care is minimizing the total amount of tax paid, which is rate*taxable income.

Just to make the point by analogy, imagine that you have two routes to drive home along, one along a highway where you get better mpg. It would be a mistake to immediately conclude that the highway is the preferable route because you gas consumption rate is lower their. If the highway is a longer route, it might mean that you consume more gallons getting home even though your mpg is better along that route.

The analogous bits are taxable rate --- mpg, and then taxable income --- miles driven.

But the pre-tax return of a given AA is fixed. Therefore if I pay less taxes I end up with more money.

False! See my post above for why.

"To play the stock market is to play musical chairs under the chord progression of a bid-ask spread."

Your post does not apply for two reasons
First, from a more analytical point of view, you have an investor starting with more money than the other.
Second, the issue in the thread is not if tax deferred accounts are better than taxable accounts, but where to keep stocks and bonds when one has both and can't put all in a tax-advantaged account.

Second, the issue in the thread is not if tax deferred accounts are better than taxable accounts, but where to keep stocks and bonds when one has both and can't put all in a tax-advantaged account.

Yes, but....the original poster then went on to ask more questions. For example, OP asked for examples of why "how much tax is paid" might not always the the right question to ask or the only question to ask.

Both you and keyhler made the same mistake: "I think what you care is minimizing the total amount of tax paid", and "Therefore if I pay less taxes I end up with more money."

These are incorrect statements. I want to be clear about that since apparently keyhler is not and I want keyhler to get correct information.

Yes, there are other factors involved in making correct decisions but everyone has to agree on the basics first.

The incontrovertible mathematical basis is that for equal return, the less taxes I pay the better.
Of course, if one gains a lot more with one solution than with the other, then more taxes paid correspond to more money made.
So, yes, you a right: minimizing taxes as an absolute rule is wrong. The best way to minimize them is to have negative returns, which actually correcpond to tax refunds!

The advice to put stocks, rather than bonds, into taxable accounts come straight from the Wiki.

If investors are trying to minimize their taxes, then this strategy is fine. But if their strategy is to maximize their after-tax wealth, it is probably sub-optimal.

The White Coat Investor has demonstrated how, when using some very simple and straightforward assumptions (e.g. stocks' will outperform bonds in terms of total return in the long-run), bonds should be placed in taxable accounts instead of stocks. There are obviously some factors that can complicate this issue, but it seems to me that the 'default' position should be that bonds go in taxable, especially in the current environment where bonds produce such little income.

This is, I think, precisely the point I am trying to raise.

It should be noted that The White Coat Investor article starts with a 50/50 allocation but never rebalance the account.

"I don't worry too much about pointing fingers at the past. I operate on the theory that every saint has a past, every sinner has a future." -- Warren Buffett

I'm beginning to question the rule of thumb that stocks should always be in taxable account. I agree that it minimizes your tax rate (in percentage) but thats not what we actually care about, correct? Don't we care about minimizing the total principal we pay to the gov (i.e. tax rate * tax income)?

Lets say bonds yield 2% real, and my marginal rate is 25%. Holding $100 of bonds in taxable brokerage means that I have after one year 100+2*.75=101.5. So my after-tax real growth rate is 1.5% if I hold bonds in taxable.

Lets say that stocks yield 5% real, and my long-term cap gains rate is 15%. Holding $100 of stocks in taxable brokerage means that I have after one year 100+5*.85=104.25. So my after-tax real growth rate is 4.25% if I hold stocks in taxable (and sold them after one year to fund expenses).

If I held the bonds in roth, I recapture 0.5% of growth per year? If I hold stocks in roth, I recapture .75% of growth per year. Doesn't that mean that, when deciding wether or not it is better to hold stocks or bonds in taxable, I have to look at the difference between the long-term capital gains rate and my marginal rate, and then also look at the expected difference between bonds and stocks growth rate?

Let me know your thoughts,

-kehyler

Edit: Let's assume that I have already filled all my tax-advantaged accounts.

If this situation was changed as follows, where should kehyler put bonds?

A long time ago, kehyler contributed to a Roth, 401k, and taxable. Today they have a balance of $100 each. Kehyler wants an AA of 80% ($240) stocks and 20% ($60) in bonds. The only 2 funds available are total stock market and total bond market (for simplicity).

For most of my investing life I have had only stocks in taxable and tax deferred accounts and stayed the course for over 30 years. I wanted and received a high total return in the end. Currently I only have taxable and Roth accounts. My taxable account has stock and muni bond funds while the Roth has stock and bond funds. I won't touch the Roth account for a long time if ever.

This year my taxable account has done better than the Roth despite spending out of taxable more than adding to it. I am beginning to think that it is foolish for me to have any bond funds in my Roth accounts at all. The chances of having any capital losses in the Roth 20 to 30 years hence is unlikely if the world keeps chugging along.

Where should the bonds go if kehyler's retirement tax bracket is 25%? 15%? Higher? (I.e. How much does this affect where bonds should go?)

In all tax brackets, I'd put the bonds in the 401k unless the bond choices were just terrible. Then I might put part of the bonds in one or both of the other accounts but at least half would still be in the 401k.

Back to misreading the advice, I think the mistake is as simple as reading "Put bonds in tax protected accounts . . ." and jumping to the unstated and illogical conclusion that stocks must go in taxable. Others have pointed out the mistake of reading past the first piece of advice, which is to maximize contributions to tax protected accounts. It is also true that under some given circumstances for some given individual the strategy should be different.

1) Assume you have two units of post-tax money. You want a 50-50 allocation to stocks/bonds.
2) You have two options: Option 1: You put 1 Unit of Stock in a Taxable Account & 1 Unit of Total Bond in a Roth
Option 2: You put 1 Unit of Stock in a Roth & 1 Unit of Tax-Exempt Bond Fund in a Taxable Account
3) To simplify we assume all dividends are qualified and taxed at a 15% rate. We assume that all stock value increase is a Long Term Capital Gain
and taxed at 15%.

4) Every year we evaluate the "true value" of our holdings. Bond Values are always true values since in either option we will only hold munis in taxable accounts. True stock values in taxable accounts are viewed as 85% of the actual amount since that is the value you would get if you pulled it out. Based on these true values, every year all accounts are rebalanced to the 50-50 allocation.

1) Assume you have two units of post-tax money. You want a 50-50 allocation to stocks/bonds.
2) You have two options: Option 1: You put 1 Unit of Stock in a Taxable Account & 1 Unit of Total Bond in a Roth
Option 2: You put 1 Unit of Stock in a Roth & 1 Unit of Tax-Exempt Bond Fund in a Taxable Account
3) To simplify we assume all dividends are qualified and taxed at a 15% rate. We assume that all stock value increase is a Long Term Capital Gain
and taxed at 15%.

4) Every year we evaluate the "true value" of our holdings. Bond Values are always true values since in either option we will only hold munis in taxable accounts. True stock values in taxable accounts are viewed as 85% of the actual amount since that is the value you would get if you pulled it out. Based on these true values, every year all accounts are rebalanced to the 50-50 allocation.

r_b=.04; annual return on bonds for the first study
r_b=.0253; annual return on bonds for the second study

I tried to utilize current numbers:

These are the results over a 30 year time period .... 4% return on Total Bond. The Blue line is Option 1. The Red line is Option 2.

Here is another run with Total Bond paying 2.53% (the current SEC Yield). Same colors for the options:

So, I'm thinking at the current low bond rate we are still better with bonds in taxable.

Excellent analysis.

There must be a fairly simple formula that could be used to determine the point at which assumed bond returns, stock returns, tax drag on stock returns, tax brackets, etc. are such that there would be no after-tax difference between putting stocks or bonds in taxable. I don't have the inclination to figure it out though.

I'm glad that I have enough tax advantaged space to never need taxable accounts.

“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

I've never thought of stock holdings as ideal for a taxable fund v tax-advantaged, but I did find myself in the position of seeing greater gains in taxable due to a small inheritance that got rolled in a few years ago in this bull market. My Roth holds Total Bond, High Yield Corporate (recently closed), Vanguard Dividend Growth and REITs. My 457b is a Wellington fund, and my 403b is fixed interest.

My taxable includes basic index funds and NY Muni bond funds plus some long term equities like Apple that I bought back when I was young and stupid about investing.

In retrospect I wish I had put VOO in my Roth alongside the usual, but I contribute so much to my retirement funds at age 50 and I'm a teacher, so my tax bracket is still low, and I've seen the benefit of holding core index funds like Total Stock in taxable, while benefiting from qualified dividends in equities. But the goal of my Roth and retirement funds is to not lose money. I can TLH in taxable if I need to.

There must be a fairly simple formula that could be used to determine the point at which assumed bond returns, stock returns, tax drag on stock returns, tax brackets, etc. are such that there would be no after-tax difference between putting stocks or bonds in taxable. I don't have the inclination to figure it out though.

I'm glad that I have enough tax advantaged space to never need taxable accounts.

Thank you. You're very kind.

You can get a "rule of thumb" for which is best by just looking at where you are true value wise after the first year. The simple algebra gives you:

There must be a fairly simple formula that could be used to determine the point at which assumed bond returns, stock returns, tax drag on stock returns, tax brackets, etc. are such that there would be no after-tax difference between putting stocks or bonds in taxable. I don't have the inclination to figure it out though.

I'm glad that I have enough tax advantaged space to never need taxable accounts.

Thank you. You're very kind.

You can get a "rule of thumb" for which is best by just looking at where you are true value wise after the first year. The simple algebra gives you:

So, in other words, what determines which goes where is whether the assumed returns on stocks is in comparison to the DIFFERENCE between the total bond and municipal bond rates.

I don't think that in general you can get a simple mathematically rigorous formula .... There are parameter values s where after a few years, the best option switches.....

I think your rule of thumb formula is sufficiently accurate to generally lead one to the best conclusion. Assumptions which may or may not hold must be made with any analysis, so I see little benefit in anything more mathematically rigorous.

“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

I'm a little confused. Why is the individual investors marginal tax bracket present in this formula? I would assume that total bond market becomes preferable to municipals at certain brackets?

Maybe we should amend the formula to include t_b, t_s to explicitly include taxes. For instance, t_b should be the marginal tax bracket one is in? t_s in your above example is the long-term cap gains rate of 0.15?

I'm a little confused. Why is the individual investors marginal tax bracket not present in this formula? I would assume that total bond market becomes preferable to municipals at certain brackets?

Maybe we should amend the formula to include t_b, t_s to explicitly include taxes. For instance, t_b should be the marginal tax bracket one is in? t_s in your above example is the long-term cap gains rate of 0.15?

I'm a little confused. Why is the individual investors marginal tax bracket not present in this formula? I would assume that total bond market becomes preferable to municipals at certain brackets?

Maybe we should amend the formula to include t_b, t_s to explicitly include taxes. For instance, t_b should be the marginal tax bracket one is in? t_s in your above example is the long-term cap gains rate of 0.15?

Remember that the analysis made some simplifying assumptions. That all dividends are qualified (and taxed at 15%) and that all stock when sold is taxed at a LTGT rate of 15%. It is assumed that in Taxable Accounts, the only bonds allowed are Tax Exempt (if one were in a zero percent tax bracket, this of course would be a bad assumption). In the Roth, the only bonds allowed are Taxable (such as Total Bond). The marginal tax of the investor doesn't really come into the calculation with those assumptions.

I did this analysis a long time ago and just put in my rates for qualified dividends and LTGT ....

I'm a little confused. Why is the individual investors marginal tax bracket not present in this formula? I would assume that total bond market becomes preferable to municipals at certain brackets?

Maybe we should amend the formula to include t_b, t_s to explicitly include taxes. For instance, t_b should be the marginal tax bracket one is in? t_s in your above example is the long-term cap gains rate of 0.15?

Remember that the analysis made some simplifying assumptions. That all dividends are qualified (and taxed at 15%) and that all stock when sold is taxed at a LTGT rate of 15%. It is assumed that in Taxable Accounts, the only bonds allowed are Tax Exempt (if one were in a zero percent tax bracket, this of course would be a bad assumption). In the Roth, the only bonds allowed are Taxable (such as Total Bond). The marginal tax of the investor doesn't really come into the calculation with those assumptions.

I did this analysis a long time ago and just put in my rates for qualified dividends and LTGT ....

pezblanco, thanks for presenting this simplified model. Reality is far more complex with many moving parts.

r_b=.04; annual return on bonds for the first study
r_b=.0253; annual return on bonds for the second study

It doesn't benefit folks in lower tax to use municipal bonds (or it benefits them less than those in highest tax brackets - hence reducing risk/reward benefits). Just looking at the highest tax bracket of 39.6%, you'd need r_b=r_m/(1-.396) to figure out your break even point. And if this is the tax bracket that determines the equilibrium, you'd expect that drives r_b to 0.0325 (assuming r_m isn't changed; in reality, it's a mix of the two). Or another way to look at current r_b=0.0253, your break even tax rate is 22.53%, so looking only at taxes and rates (i.e. ignoring risks), many more folks should be buying tax-exempt munis or demanding more return for the taxable bonds. QE effects may be partly responsible for lower bond returns and as it's withdrawn, we may head back towards equilibrium. Anyway, at current rates, both methods lead to municipal bonds in taxable, making the decision easy. When the recommended action diverges, you have to look deeper at your assumptions and expectations.

I'm a little confused. Why is the individual investors marginal tax bracket not present in this formula? I would assume that total bond market becomes preferable to municipals at certain brackets?

Maybe we should amend the formula to include t_b, t_s to explicitly include taxes. For instance, t_b should be the marginal tax bracket one is in? t_s in your above example is the long-term cap gains rate of 0.15?

Remember that the analysis made some simplifying assumptions. That all dividends are qualified (and taxed at 15%) and that all stock when sold is taxed at a LTGT rate of 15%. It is assumed that in Taxable Accounts, the only bonds allowed are Tax Exempt (if one were in a zero percent tax bracket, this of course would be a bad assumption). In the Roth, the only bonds allowed are Taxable (such as Total Bond). The marginal tax of the investor doesn't really come into the calculation with those assumptions.

I did this analysis a long time ago and just put in my rates for qualified dividends and LTGT ....

pezblanco, thanks for presenting this simplified model. Reality is far more complex with many moving parts.

r_b=.04; annual return on bonds for the first study
r_b=.0253; annual return on bonds for the second study

It doesn't benefit folks in lower tax to use municipal bonds (or it benefits them less than those in highest tax brackets - hence reducing risk/reward benefits). Just looking at the highest tax bracket of 39.6%, you'd need r_b=r_m/(1-.396) to figure out your break even point. And if this is the tax bracket that determines the equilibrium, you'd expect that drives r_b to 0.0325 (assuming r_m isn't changed; in reality, it's a mix of the two). Or another way to look at current r_b=0.0253, your break even tax rate is 22.53%, so looking only at taxes and rates (i.e. ignoring risks), many more folks should be buying tax-exempt munis or demanding more return for the taxable bonds. QE effects may be partly responsible for lower bond returns and as it's withdrawn, we may head back towards equilibrium. Anyway, at current rates, both methods lead to municipal bonds in taxable, making the decision easy. When the recommended action diverges, you have to look deeper at your assumptions and expectations.

Good points!!! Thank you for your thoughts. As far as investors in lower tax brackets are concerned ... if we are at or below the 15% tax bracket, qualified dividends and LTGT aren't taxed at all. In that setting, the investor should never use munis .... they can just put Total Bond in their taxable account if they wish. In this setting, the two options give identical results ....

1) Assume you have two units of post-tax money. You want a 50-50 allocation to stocks/bonds.
2) You have two options: Option 1: You put 1 Unit of Stock in a Taxable Account & 1 Unit of Total Bond in a Roth
Option 2: You put 1 Unit of Stock in a Roth & 1 Unit of Tax-Exempt Bond Fund in a Taxable Account

These assumptions bias the study in favor of option 2 (bonds in taxable), because option 2 has more risk; the IRS will share some of your unexpected stock gains or losses if stocks are in a taxable account. I prefer to do this type of comparison assuming a traditional IRA, as the IRS takes about the same proportion of gains in a traditional IRA or a stock account.

3) To simplify we assume all dividends are qualified and taxed at a 15% rate. We assume that all stock value increase is a Long Term Capital Gain
and taxed at 15%.

4) Every year we evaluate the "true value" of our holdings. Bond Values are always true values since in either option we will only hold munis in taxable accounts. True stock values in taxable accounts are viewed as 85% of the actual amount since that is the value you would get if you pulled it out.

This incorrectly favors bonds in a taxable account, since the 15% capital-gains tax is paid only on the gain, not on the original investment or reinvested dividends.

Based on these true values, every year all accounts are rebalanced to the 50-50 allocation.

A good idea, but as above, this makes the portfolio with stocks in the Roth IRA somewhat riskier.

These numbers are current yields (as of the date of the study; Vanguard Intermediate-Term Tax-Exempt now yields 1.99%, or 2.09% on Admiral shares)

r_b=.04; annual return on bonds for the first study
r_b=.0253; annual return on bonds for the second study

but the first study is unreasonable. If taxable bonds return 4%, then munis should have a yield higher than 1.96%. The 2.53% on Total Bond Market in the second study suggests that the risks are close. My rule of thumb is that munis have 75% of the yield of taxable bonds of comparable risk, which would be 2.61% for a muni yield of 1.96%.